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Optimal decay estimate of mild solutions to the compressible Navier‐Stokes‐Korteweg system in the critical Besov space
Author(s) -
Wang YuZhu,
Wang Yinxia
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5316
Subject(s) - mathematics , besov space , compressibility , space (punctuation) , mathematical analysis , energy (signal processing) , initial value problem , energy method , operator (biology) , value (mathematics) , physics , statistics , thermodynamics , interpolation space , biochemistry , chemistry , linguistics , philosophy , repressor , functional analysis , transcription factor , gene
In this paper, we consider the initial value problem for the compressible Navier‐Stokes‐Korteweg system in several space variables. Optimal decay estimate of mild solutions in the critical Besov spaces is established. The proof is based on the decay estimate of solutions operator in the low‐frequency region and the energy estimate in the high‐frequency region.